PhD Chapter 3
Results 1/3
This series of files compile all analyses done during Chapter 3:
- Section 1 presents the calculation of the indices of exposure.
- Section 2 presents variable exploration and regressions results.
- Section 3 presents species distribution models.
All analyses have been done with R 4.1.2.
Click on the table of contents in the left margin to assess a specific analysis.
Click on a figure to zoom it
1. Maps
1.1. General map
1.2. Parameters maps
Maps of abiotic habitat variables:
Depth
Slope
River CDOM
2. Modelling the influence of human activities
We computed an exposure index for each category of human activity, which we will use for regression models and SDM (see Section 2). Two types of exposure index were calculated seperately, one for land- and sea-based activities and one for fisheries, and a cumulative exposure index integrated all this information in a unique metric.
Categories of human activity considered in the Baie des Sept Îles:
- aquaculture: mussel farm (AquaInf)
- dredging: collection zones, dumping zones (DredColl, DredDump)
- land-based:
- diffusive runoff (CityInf, InduInf)
- sewers (SewRain, SewWast)
- artificial structures (CityWha, InduWha)
- shipping: anchor sites, traffic routes (ShipMoor, ShipTraf)
- fisheries: dredges, nets, traps, bottom-trawls (FishDred, FishNet, FishTrap, FishTraw)
2.1. Individual exposure indices
2.1.1. Land- and sea-based activities
The following map present the sources of land- and sea-based human activities considered here. For each activity, we calculated an index of exposure \(E_{ij}\).
Principle
To calculate the exposure index \(E_{ij}\), we modelled the diffusion of theoretical particles in the ecosystem. Particles are the resultant of an activity, such as contaminants or sediment, and they diffuse from the source of the activity. This method is not based on a circulation model, because such tool is not yet available in the Baie des Sept Îles.
An identical number of particles is released by each source of activity. The exposure score is based on the density of particles in the environment after diffusion from the source(s) of activity: locations far from the source have a low density of particles (i.e. low probability to receive particles), resulting in low exposure (and vice versa). Thus, exposure is proportional to the distance from the source \(D_{ij}\).
The example above is illustrated with a linear relationship. However, we will use another spatial function where particle archetypes have unique parameters to account for a specific diffusion behaviour. This function \(f\), called here the decay function, will compute the final exposure index based on \(D_{ij}\).
Methodology
Distance from the source
\(D\) is calculated with a
least-cost pathfinding algorithm from the R package
gdistance, by establishing a connectivity model based on a
‘resistance seascape’ concept. We created a 100 x 100 m raster whose
cell can be selected to obtain the path connecting start (source of the
activity) and end (each raster cell) points. Journey between two
neighbour cells has a cost to be included in this path, which is
dependant on several constraints. The length of the final path then
gives distance \(D_{ij}\).
We considered three underlying principles for the physical constraints:
- marine ecosystems: particles cannot disperse on land
- gravity: particles disperse easily from shallow to deeper depths while the reverse is difficult
- hydrodynamism: particles disperse according to local hydrodynamical currents
The connectivity model thus included: (i) coasts as boundaries
delimitating cells unselectable by the algorithm, (ii) bathymetry, (iii)
river plumes as hydrodynamical fronts with an intensity and a direction
(a complete circulation model in BSI is not yet available). These
constraints were implemented in the transition function \(t\), used by costDistance()
when creating the least-cost path (chess queen configuration):
- land is set with a connectivity of 0
- bathymetry is compared between two cells:
- when point A is shallower than point B, connectivity is highest
- when point A is deeper than point B, connectivity is lower
- CDOM content (proxy of hydrodynamism) is compared between two cells
The equation for \(D_{ij}\) is:
\[ D_{ij} = t(S_{j}, G_{i}, B_{i}, H_{i}) \]
- \(t\) is the transition function
- \(S_{j}\) is the source(s) of activity
- \(G_{i}\) is the geography component (coastline)
- \(B_{i}\) is the bathymetry component
- \(H_{i}\) is the hydrodynamics component (CDOM proxy)
- \(i\) is a cell
- \(j\) is a human activity
⚠️ For now, the hydrodynamics constraint is not implemented.
Exposure
With \(D_{ij}\) calculated, we can compute \(E_{ij}\) with the decay function. To this end, we used a gaussian kernel function (exponential quadratic relationship), which is a way to consider diffusion in a 2D environment:
\[ E_{ij} = exp\left(C . a_{j} . (D_{ij} - b_{j})^2 + c_{j} \right) \]
- \(C\) is a constant
- \(a_{j}\), \(b_{j}\), \(c_{j}\) are parameters of the decay function
- \(D_{ij}\) is the distance from the source
- \(i\) is a cell
- \(j\) is a human activity
The constant \(C\) is set to 0.000025, linked to the spatial extent of the study area (\(range\) = 25000 m). The general equation to set \(C\) would be:
\[ C = \frac{1}{range} \]
We considered five decay functions to model different diffusion behaviours for human activities. To do so, we modified parameters of this function, in particular \(a_{j}\) (\(b_{j}\) and \(c_{j}\) are set to 0):
- Type I: very localized ( purple curve, \(a_{j}\) = -1)
- Type II: localized ( blue curve, \(a_{j}\) = -0.1)
- Type III: diffused ( green curve, \(a_{j}\) = -0.01)
- Type IV: very diffused ( yellow curve, \(a_{j}\) = -0.001)
- Type V: ubiquitous ( red curve, \(a_{j}\) = -0.0001)
To assign a type of decay function to a human activity, we performed a litterature review describing the drivers related to each considered human activity and how can we model them best (details will be available in the final version of the article). Based on this work, here are the results:
| AquaInf | DredColl | DredDump | CityInf | InduInf | SewRain | SewWast | CityWha | InduWha | ShipMoor | ShipTraf |
|---|---|---|---|---|---|---|---|---|---|---|
| II | II | II | III | III | IV | IV | III | III | II | III |
Results
The following maps present the values of \(E_{ij}\) for land/sea-based activities (grey = low exposure; dark blue = high exposure).
Aquaculture
Dredging
Runoff
Sewers
Structures
Shipping
2.1.2. Fisheries
These data belong to Department of Fisheries and Oceans Canada, with a permission granted to David Beauchesne. As such, we cannot present raw products and we will only work on derived data.
Here, \(E_{ij}\) have been calculated with a proxy based on fisheries data for each gear used in the area.
Methodology
We extracted data from a global database for the St. Lawrence, for all fishing events occuring within the Baie des Sept-Îles. Four types of gears (traps, bottom-trawls, nets and dredges) have been considered in the bay between 2010 and 2015. Eight species have been gathered, with data expressed as number of fishing events or kilograms of collected individuals for each gear:
| Gear | Code | Years | Events | Species |
|---|---|---|---|---|
| Dredge | FishDred | 2010-2014 | 21 | Mactromeris polynyma |
| Net | FishNet | 2010 | 5 | Clupea harengus, Gadus morhua |
| Trap | FishTrap | 2010-2015 | 1061 | Buccinum sp., Cancer irroratus, Chionoecetes opilio, Homarus americanus |
| Bottom-trawl | FishTraw | 2013-2014 | 2 | Pandalus borealis |
As each gear was not used consistently during this period, we averaged the number of fishing events to obtain a proxy of fishing intensity. Furthermore, we modified this proxy with a smoothing function in order to ‘diffuse’ the signal around the actual event.
Results
The following maps present the values of \(E_{ij}\) for fisheries (grey = low exposure; dark blue = high exposure):
Here are the maps for each gear:
Dredge
Net
Trap
Bottom-trawling
2.2. Cumulative exposure index
We can combine individual exposure indices into a unique value, the cumulative exposure index \(CE_{i}\), here with an additive relationship. This score varies between 0 and 7, being the number of considered human activities, and its equation is:
\[ CE_{i} = \sum_{j} E_{ij} \]
⚠️ Future iterations of this score will try different link functions to account for non-additive effects.
The cumulative exposure index may been represented into five classes, according to principles from the Marine Strategy Framework Directive:
- indigo = lowest exposure (\(E_{ij}\) < 1.4) ~ high status
- green = low exposure (1.4 ≤ \(E_{ij}\) < 2.8) ~ good status
- yellow = moderate exposure (2.8 ≤ \(E_{ij}\) < 4.2) ~ moderate status
- orange = high exposure (4.2 ≤ \(E_{ij}\) < 5.6) ~ poor status
- crimson = highest exposure (\(E_{ij}\) ≥ 5.6) ~ bad status
Maximum detected cumulative exposure is 3.698.
This histogram represents the number of stations falling in each class:
These scores will be used for the species distribution models (see Section 3).